Page 246 - Design and Operation of Heat Exchangers and their Networks

236 Design and operation of heat exchangers and their networks

or in a matrix form:

0
0
0
T ¼ G T + GT 00 (6.19)
E E
00 000 0 00 00
T ¼ G T + G T E (6.20)
T T
0 0 0 0 00 00 00 00
½
where T ¼ t t ⋯ t Š and T ¼ t ½ 1 t 2 ⋯ t N 00 Š are the entrance
2
1
N
0
and exit stream temperatures of the network, respectively.
As has been shown in Section 3.6, substituting Eq. (6.13) into
Eqs. (6.19), (6.20), we can explicitly express the inlet and outlet fluid tem-
peratures of individual heat exchangers and the exit stream temperatures of
the network with Eqs. (6.21), (6.13), (6.22), respectively.
0 1 0 0
T ¼ I GVð Þ G T (6.21)
E
1
00
000
000
00
00
0
0
00
T ¼ G T + G T ¼ G + G VI GVÞ G T 0 (6.22)
ð
E
Because Eqs. (6.21), (6.22) contain the calculation of an N N inverse
matrix, for a large heat exchanger network, more computing time might be
required. As an alternative, the “upwind” iterative calculation method is
recommended. The convergence of the iteration is ensured by alternately
recalculating the temperatures of the hot/cold process streams with fixed
cold/hot stream temperatures.
(1) At the beginning, set all unknown inlet and outlet temperatures of the
hot and cold process streams equal to their supply temperatures of the
network.
(2) Starting from the network entrances of the hot process streams and
along the stream flow direction, calculate the outlet temperature of
hot stream in each heat exchanger according to its known or assumed
inlet temperature of the hot and cold streams but do not calculate the
outlet temperature of the cold stream.
(3) Starting from the network entrances of the cold process streams and
along the stream flow direction, calculate the outlet temperature of cold
stream in each heat exchanger according to its known or calculated inlet
temperature of the hot and cold streams but do not calculate the outlet
temperature of the hot stream.
(4) Repeat Steps (2) and (3) to correct the outlet temperatures of hot and
cold streams, respectively, until the given accuracy is achieved.